If I understand right, permission of /home says that only root can add/delete files (or directories) in this directory, but then there's the directory test1 which has user1 as its owner. That means that user user1 can add/delete files (or directories) in /home/test1. Does this mean that directory permission of /home is only valid till its immediate children and not its all descendants (grandchildren and so on)?

And it must be only root who let user1 be the owner of its child /home/test1 and from then on, user1 can control owners of its children (and all descendants)?

The directory permission of home is only valid for itself. Once user1 has permissions on a directory it can do anything, including create subdirectories. So, once there is a directory under home that user1 has permissions on, it user1 can add anything to that directory.

However, if a directory under user1 was to be owned by another user, then user1 would only have world permissions on that directory.